Hadron multiplicity in pp and AA collisions at LHC from the Color Glass Condensate

TL;DR

The paper addresses predicting charged-hadron multiplicities in $pp$ and $AA$ collisions at LHC within the color-glass condensate (CGC) framework. It implements a $k_T$-factorized approach with an impact-parameter dependent saturation scale $Q_A(x;b)$ and an unintegrated gluon density tied to the forward dipole amplitude via BK evolution, calibrated to HERA DIS data. By fixing two soft-scale parameters at RHIC, it delivers quantitative predictions for central Pb-Pb collisions at $\sqrt{s}=2.75$ and $5.5$ TeV (e.g., $dN_{ch}/d\eta|_{\eta=0} \approx 1152 \pm 81$ and $1314 \pm 92$) with uncertainties below $7\%$, and it contrasts with KLN predictions while aligning with early LHC $pp$ measurements. The results test the universality of saturation physics and offer a concrete benchmark for CGC-based descriptions of high-energy hadronic collisions.

Abstract

We provide quantitative predictions for the rapidity, centrality and energy dependencies of inclusive charged-hadron productions for the forthcoming LHC measurements in nucleus-nucleus collisions based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives very good descriptions of the first data from the LHC for the inclusive charged-hadron production in proton-proton collisions, the deep inelastic scattering at HERA at small Bjorken-x, and the hadron multiplicities in nucleus-nucleus collisions at RHIC.

Figures (5)

• Figure 1: The impact parameter dependence of the saturation scale for proton and lead at $x = 10^{-3}$ and $x=10^{-5}$.
• Figure 2: Top: The effect of the soft-scale $\mu$ is shown at $\sqrt{s}=200$ GeV. Lower: Pseudo-rapidity distribution of charged particles produced in Au-Au and Pb-Pb central $0-6\%$ collisions at RHIC $\sqrt{s}=19.6, 130, 200$ GeV and the LHC energies $\sqrt{s}=2.75, 5.5$ TeV. The band indicates less than $3\%$ theoretical error coming from uncertainties related to normalization and modeling the mini-jet mass. The experimental data are from PHOBOS collaboration rhic1.
• Figure 3: The pseudo-rapidity dependence at RHIC $\sqrt{s}=200$ GeV (top) and the LHC $\sqrt{s}=5.5$ TeV (lower) at different centrality bins. The band indicates less than $3\%$ theoretical errors. The experimental data are from PHOBOS collaboration rhic1.
• Figure 4: Energy dependence of the charged hadrons multiplicity at midrapidity $\eta=0$ in central collisions in $pp$ and $AA$ collisions. The theoretical curve Saturation model (LR) is our prediction. The band indicates less than $3\%$ theoretical errors. The total theoretical uncertainties is less than $7\%$, see the text for the details. We also show the KLN prediction KLNLHC with the same error band as ours. The experimental data are from CMSCMS2ALICErhic1ppdata.
• Figure 5: The scaled pseudo-rapidity density as a function of number of participant $N_{par}$ at midrapidity for Au-Au at $\sqrt{s}=130, 200$ GeV and for Pb-Pb at $\sqrt{s}=5.5$ TeV. The experimental data are from PHOBOS collaboration rhic2.